Spatio-temporal models
Many real-world data sets vary in both space and time.
We often want to model how similarity (correlation) changes across both dimensions.
The good news 👍
The bad news 👎
fully spatio-temporal models are complex
model fitting can take a long time
different types of spatio-temporal data structures lead to different types of complexities
additional dependencies: in space and time
spatial and temporal behaviour can be independent on each other, or dependent: i.e. properties of the spatial structure vary through time (or vice versa)
Several options are available in inlabru
Areal Model
Geostatistical and Point Process models
\(\frac{\text{Number of cases } Y_{st}}{\text{Expected numer of cases }E_{st}}\) in Ohio from 1968 to 1988
Space
\(\frac{\text{Number of cases } Y_{st}}{\text{Expected numer of cases }E_{st}}\) in Ohio from 1968 to 1988
Time
\(\frac{\text{Number of cases } Y_{st}}{\text{Expected numer of cases }E_{st}}\) in Ohio from 1968 to 1988
Time
The observation model \[ Y_{st}|\lambda_{st}\sim\text{Poisson}(E_{st}\lambda_{st}) \]
We are going to see different models for the linear predictor \(\eta_{st} = \log \lambda_{st}\)